rm files owned by root?

Hi all,
I'm seriously troubled by behaviour of my system I just encountered:
If i do (as root):
touch /home/user/a
Then (as user);
rm /home/user/a
It asks if I want to remove this file, since it's write protected. If I say "y", then the file gets deleted. But it shouldn't be! Should it?
(Sorry if this is a dumb question.)
Hope you can help,
Raphael from Swizerland
--
dekkker at gmx dot ch